The present invention relates generally to wireless communications systems and, in particular, to wireless communications systems based on code division multiple access (CDMA).
The well known system of Walsh Hadamard functions H (of length 2n, where n is a positive integer) form an orthogonal basis for the Euclidean space R2n and have range one and minus one. These functions have found application in the CDMA area for wireless communication. More recently, systems of Quasi-Walsh functions Q were introduced for application in CDMA wireless communication systems. These functions, having similar properties as the Walsh functions, also form an orthogonal basis for R2n and attain only values one and minus one. The systems of Quasi-Walsh functions are formed by negating arbitrarily specified tuples of Walsh Hadamard functions. In terms of matrix operations, the systems of Quasi-Walsh functions Q are row vectors obtained by post multiplying the Walsh Hadamard matrix H by a diagonal matrix D, which is comprised of ones and minus onesxe2x80x94i.e., Q=H D. Note that the values in each row vector represents a chip. This matrix representing Quasi-Walsh functions Q is a length preserving transformation called an isometry, or an orthonormal transformation, in this case where the underlying field is real valued. Since the Walsh Hadamard matrix is orthogonal along with the diagonal matrix D, the resulting product matrix Q is also orthogonal. Accordingly, distinct row vectors in Q, i.e., distinct Quasi-Walsh functions, have an inner product of zero. Note that when the diagonal matrix D is an identity matrix L the Walsh Hadamard matrix appears. Therefore, Walsh Hadamard matrix H is a special case of the Quasi-Walsh matrix when D=I.
The present invention utilizes systems of Quasi-Walsh functions for high resilience against interception and jamming in addition to allowing multiple access and acquisition. The present invention switches among generalized systems of Quasi-Walsh functions at some rate r, where r may either be a fixed or variable value not equal to zero. The present invention transmits a first set of information for a user over a communication channel using a first code, and transmits a second set of information for the user over the communication channel using a second code in place of the first code, wherein the first and second codes may be orthogonal codes or encryption codes and the communication channel has a fixed or variable datarate. The first and second codes may be indicated using an index, such as a pseudo-random sequence, an algorithm, a mathematical equation, a known or cyclical sequence, etc., wherein the index may be single or multi-valued. In one embodiment, the first and second codes correspond to row vectors i and j in a first and second systems of orthogonal functions. The row vectors i and j may be identical or different in their respective systems of orthogonal functions. Likewise, the first and second systems of orthogonal functions may be identical or different, and may be systems of Quasi-Walsh functions.